EXACT PROPERTIES OF McNEMAR'S TEST IN SMALL SAMPLES

Abstract

The exact distribution of McNemar's test statistic is used to determine critical pOints for two-sided tests of equality of marginal proportions in the correlated 2x2 table. The result is a conservative unconditional test which reduces to the conditional binomial test as a special case. Exact critical points are given for the significance levels 0.05, 0.01 and 0.001 with the sample sizes n=6(1)50. A computer program for tail probabilities makes the calculation of power easy. It is concluded that McNemar's test is never inferior to the conditional binomial test and that much can be gained by using the McNemar test if the main purpose is to detect differences between the marginal proportions in small samples. A further conclusion is that the chi-square approximation of McNemar's test statistic may be inadequate when n<=50. Especially the 5% critical points are constantly too small.